A059129 A hierarchical sequence (W2{2}* - see A059126).

1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 4, 3, 1, 2, 1, 2, 3, 2, 1, 2, 1, 4, 5, 4, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 4, 3, 1, 2, 1, 2, 3, 2, 1, 2, 1, 5, 6, 5, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 4, 3, 1, 2, 1, 2, 3, 2, 1, 2, 1, 4, 5, 4, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 4, 3, 1, 2, 1, 2, 3, 2, 1, 2, 1, 6, 7, 6, 1, 2, 1, 2, 3, 2, 1, 2, 1

Offset: 0

Author

Jonas Wallgren, Jan 19 2001

Keywords

• easy
• nonn

Comments

Begin with the empty finite sequence s_0. Inductively extend s_n to obtain s_{n+1} as follows: if s_n is given by a, b, c, ..., d, e, f, with g being the least integer that is not a value of s_n, then s_{n+1} is a, b, c, ..., d, e, f, g, -f, -e, -d, ..., -c, -d, -a, -g. The terms of {a(n)} give the absolute values of the limit of these sequences. These finite sequences naturally describe elements of fundamental groups occurring in picture-hanging puzzles and Brunnian links. - Thomas Anton, Oct 15 2022

Links

• Jonas Wallgren, Hierarchical sequences
• E. D. Demaine, M. L. Demaine, Y. N. Minsky, J. S. B. Mitchell, R. L. Rivest, and M. Patrascu, Picture-Hanging Puzzles, arXiv:1203.3602, [cs.DS], 2012-2014.

Crossrefs

Cf. A034947, A059126.